NDLI: Robust Linear Regression Analysis

Content Provider	IEEE Xplore Digital Library
Author	Papageorgiou, G. Bouboulis, P.
Copyright Year	1991
Abstract	The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical (considered nowadays) methods, recently, it has attracted more attention in the context of sparse modeling, where several notable contributions have been made. In the present manuscript, a new approach is considered in the framework of greedy algorithms. The noise is split into two components: a) the inlier bounded noise and b) the outliers, which are explicitly modeled by employing sparsity arguments. Based on this scheme, a novel efficient algorithm (Greedy Algorithm for Robust Denoising-GARD), is derived. GARD alternates between a least square optimization criterion and an Orthogonal Matching Pursuit (OMP) selection step that identifies the outliers. The case where only outliers are present has been studied separately, where bounds on the Restricted Isometry Property guarantee that the recovery of the signal via GARD is exact. Moreover, theoretical results concerning convergence as well as the the recovery of the support of the sparse outlier vector and derivation of error bounds in the case of additional bounded noise are discussed. Finally, we provide extensive simulations, which demonstrate the comparative advantages of the new technique.
Sponsorship	IEEE Signal Processing Society
Starting Page	3872
Ending Page	3887
Page Count	16
File Size	3968918
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	15
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robustness Noise Matching pursuit algorithms Signal processing algorithms Greedy algorithms Linear regression Mathematical model robust regression Greedy Algorithm for Robust Denoising (GARD) greedy algorithms OMP for outlier detection outlier detection robust least squares robust orthogonal matching pursuit
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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